as \(b \rightarrow 0^+\) . These results are contained in Theorems REF  and REF  below. Provided that the final time is short enough, the smallness conditions on the initial data can be imposed in a lower-order norm than the one needed in the energy analysis. We expect these estimates to be of practical relevance in numerical simulations of quasilinear waves, where artificial dissipation is commonly introduced to combat the spurious oscillations that arise as the wavefront steepens, also known as Gibbs oscillations; cf. [1]}, [2]}. As a by-product of our analysis, we also address the questions of local well-posedness of (REF ) and (REF ) on bounded domains for \(b \ge 0\) , which, to the best of our knowledge, have not been answered before for \(b=0\)  in the Kuznetsov case (REF ). Further, compared to the existing result on analysis of the inviscid Westervelt equation [3]}, we allow for arbitrarily large data in \(H^2(\Omega ) \times H^1(\Omega )\) , as relevant in practical ultrasonic applications. We point the readers to Theorems REF  and REF  below for the respective results.
